cospectrum

Functions

cospectrum

Compute power spectrum or co-spectrum of atmospheric time series.
cospectrum.cospectrum(ini, x, y, f, mean_wind_speed, plot=False, filename='', spectrum_type='')[source]

Compute power spectrum or co-spectrum of atmospheric time series.

This function calculates either the power spectrum (when x=y) or the co-spectrum (when x≠y) of atmospheric time series data. It implements standard eddy covariance spectral analysis techniques, including normalization and scaling according to Kaimal et al. (1972) conventions.

Parameters:

  • ini (dict) –

    Initialization dictionary containing:

    • param.WINDOW_LENGTHfloat

      Length of the averaging window in seconds

    • param.SAMPLING_RATE_FINALfloat

      Final sampling rate in Hz

    • param.NUM_FREQ_BINSint

      Number of frequency bins for log-averaging

    • param.SENSOR_HEIGHTfloat

      Height of the sensor above ground [m]

  • x (numpy.ndarray) – Fluctuations of the first time series. For power spectrum, this is the only relevant time series. Units: Variable-specific (e.g., m s⁻¹ for wind, ppb for concentrations)

  • y (numpy.ndarray) – Fluctuations of the second time series. For power spectrum, should be identical to x. Units: Variable-specific

  • f (numpy.ndarray) – Frequency axis of spectra [Hz]

  • mean_wind_speed (float) – Mean wind speed used for normalization [m s⁻¹]

  • plot (bool, optional) – If True, creates diagnostic plots of the (co)spectra

  • filename (str, optional) – Name of the file being processed, used in plot titles

  • spectrum_type ({'spec', 'cospec'}, optional) – Type of analysis being performed: - ‘spec’: power spectrum - ‘cospec’: co-spectrum

Returns:

  • cospec_xy (numpy.ndarray) – Log-bin averaged (co)spectrum Co(x’,y’,f) Units: Product of input variable units per Hz

  • cospec_xy_scaled (numpy.ndarray) – Normalized and frequency-scaled (co)spectrum f·Co(x’,y’,f)/xy Units: Dimensionless

  • cospec_xy_integral (float) – Integral of the (co)spectrum, equals covariance for co-spectrum or variance for power spectrum Units: Product of input variable units

Notes

The function follows standard procedures for spectral analysis in micrometeorology:

  1. Computes two-sided spectrum using FFT

  2. Extracts and scales the one-sided spectrum

  3. Log-bins the results for clearer visualization

  4. Normalizes by integral and scales by frequency

For co-spectra, the results can be compared to the Kaimal formulations for unstable conditions when properly normalized.

See also

logBinSpectrum

Log-binning of spectral data

theor_cosp_Kaimal

Theoretical Kaimal co-spectrum

References

Examples

>>> # Calculate power spectrum of vertical wind speed
>>> w = np.random.randn(18000)  # 30 minutes at 10 Hz
>>> f = np.fft.fftfreq(18000, d=0.1)[:9000]  # Positive frequencies only
>>> ini = {'param': {
...     'WINDOW_LENGTH': 1800,
...     'SAMPLING_RATE_FINAL': 10,
...     'NUM_FREQ_BINS': 50,
...     'SENSOR_HEIGHT': 23.5
... }}
>>> spec, spec_scaled, variance = cospectrum(
...     ini, w, w, f, 2.5, plot=True,
...     spectrum_type='spec'
... )

Author

Written by Bernard Heinesch (December 2022) University of Liege, Gembloux Agro-Bio Tech Updated July 2024: Added power spectrum functionality